Problem: Solve for $x$ and $y$ using substitution. ${3x-4y = 11}$ ${x = -4y+9}$
Solution: Since $x$ has already been solved for, substitute $-4y+9$ for $x$ in the first equation. ${3}{(-4y+9)}{- 4y = 11}$ Simplify and solve for $y$ $-12y+27 - 4y = 11$ $-16y+27 = 11$ $-16y+27{-27} = 11{-27}$ $-16y = -16$ $\dfrac{-16y}{{-16}} = \dfrac{-16}{{-16}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {x = -4y+9}\thinspace$ to find $x$ ${x = -4}{(1)}{ + 9}$ $x = -4 + 9$ ${x = 5}$ You can also plug ${y = 1}$ into $\thinspace {3x-4y = 11}\thinspace$ and get the same answer for $x$ : ${3x - 4}{(1)}{= 11}$ ${x = 5}$